Microstructural Topology Research Articles

Microstructural topology optimization for minimizing the sound pressure level of structural–acoustic coupled systems with multi-scale random parameters

ABSTRACTThe main aim of this article is to present a robust microstructural topology optimization methodology for structural–acoustic coupled systems with multi-scale random parameters. During the microstructural topology optimization, both the uncertainty at the macro-scale, which comes from the physical parameters of the acoustic medium or the external load, and the uncertainty existing in the constituent material properties of the microstructure at the micro-scale are considered as random parameters. A homogenization-based probabilistic finite element method (HPFEM) is first developed for quantifying the structural–acoustic system with multi-scale random parameters. The use of the HPFEM transforms the problem of microstructural topology optimization with multi-scale random parameters to an augmented deterministic microstructural topology optimization problem. This provides a computationally cheap alternative to Monte Carlo-based optimization algorithms. A numerical example of a hexahedral box is given to demonstrate the efficiency of the proposed method.

Multiscale concurrent topology optimization for cellular structures with multiple microstructures based on ordered SIMP interpolation

This paper presents a novel multiscale concurrent topology optimization method for cellular structures with various types of microstructures to obtain a superior structural performance at an affordable computation cost. At macroscale, different microstructures are regarded as different materials in a multi-material topology optimization. An ordered solid isotropic material with penalization (SIMP) interpolation model, which is efficient for solving multi-material topology optimization problems without introducing any new variables, is employed to generate an overall structure layout with predetermined multiple materials. At microscale, each macroscale element is viewed as an individual microstructure. All macroscale elements with the same material are represented by a unique microstructure. A parametric level set method (PLSM) is applied to evolve the shape and topology of the representative microstructures, whose effective properties are evaluated by a numerical homogenization method. The connectivity of adjacent microstructures is guaranteed by a kinematical connective constraint. Using the proposed method, the macrostructural topology as well as the locations and configurations of microstructures can be simultaneously optimized. Numerical examples are provided to test the effectiveness of the proposed method.

An anisotropic damage model for tensile fatigue

AbstractFatigue damage in materials is considered to be the effect of material degradation, and the dispersion in fatigue life is attributed to variability in microstructure. This paper presents a numerical model to simulate fatigue damage evolution using continuum damage mechanics to characterize material degradation. An explicit microstructure topology representation is achieved using Voronoi tessellations. Unlike conventional models which use a scalar approximation for damage, this model treats the damage variable as an anisotropic tensor. The model is used to simulate tensile fatigue failure in thin steel specimen. The fatigue life estimations from the model compares well with published experimental results. The results predict a high variability in fatigue life that is characteristic of metals and alloys, as compared with the existing isotropic damage models available in the literature. The model was also used to study the influence of material inhomogeneity on fatigue life dispersion.

Three-Phase Microstructure Topology Optimization of Two-Dimensional Phononic Bandgap Materials Using Genetic Algorithms

The bandgap, an important characteristic of the periodic structure, is dispersion-related, which can be designed by tailoring the layout of materials within the periodic microstructures. A typical example of a periodic structure is phononic crystals (PnCs), which are traditionally fabricated from two-phase materials. Herein, we investigate the topologies of periodic three-phase PnCs. The microstructures of the three-phase PnCs are optimized using a two-stage genetic algorithm, and three case studies are proposed to obtain the following: (1) the maximum relative bandgap width, (2) the maximum absolute bandgap width, and (3) the maximum bandgap at a specified frequency. More importantly, the three-phase material provides significant advantages compared to the typical two-phase materials, such as a low-frequency bandgap. This research is expected to contribute highly to vibration and noise isolation, elastic wave filters, and acoustic devices.

Microstructural topology optimization of viscoelastic materials of damped structures subjected to dynamic loads

This paper presents microstructural topology optimization of viscoelastic materials for damped structures. The microstructure is composed of periodic unit cells. The effective modulus of the viscoelastic material is obtained through the homogenization method. The density-based topology optimization is adopted to find optimal microstructures of viscoelastic materials. The design objective is to effectively attenuate transient responses of damped structures. Transient responses are evaluated with an implicit time integration scheme based on the two-scale analysis. An adjoint sensitivity analysis is developed for computation of the derivatives of transient responses of macrostructures with respect to microstructural design variables. Several numerical examples demonstrate the effectiveness of the proposed approach. Various microstructures of viscoelastic materials are presented, and their corresponding transient responses of the damped structures are discussed.

Design of material microstructures for maximum effective elastic modulus and macrostructures

PurposeIn pure material design, the previous research has indicated that lots of optimization factors such as used algorithm and parameters have influence on the optimal solution. In other words, there are multiple local minima for the topological design of materials for extreme properties. Therefore, the purpose of this study is to attempt different or more concise algorithms to find much wider possible solutions to material design. As for the design of material microstructures for macro-structural performance, the previous studies test algorithms on 2D porous or composite materials only, it should be demonstrated for 3D problems to reveal numerical and computational performance of the used algorithm.Design/methodology/approachThe presented paper is an attempt to use the strain energy method and the bi-directional evolutionary structural optimization (BESO) algorithm to tailor material microstructures so as to find the optimal topology with the selected objective functions. The adoption of the strain energy-based approach instead of the homogenization method significantly simplifies the numerical implementation. The BESO approach is well suited to the optimal design of porous materials, and the generated topology structures are described clearly which makes manufacturing easy.FindingsAs a result, the presented method shows high stability during the optimization process and requires little iterations for convergence. A number of interesting and valid material microstructures are obtained which verify the effectiveness of the proposed optimization algorithm. The numerical examples adequately consider effects of initial guesses of the representative unit cell (RUC) and of the volume constraints of solid materials on the final design. The presented paper also reveals that the optimized microstructure obtained from pure material design is not the optimal solution any more when considering the specific macro-structural performance. The optimal result depends on various effects such as the initial guess of RUC and the size dimension of the macrostructure itself.Originality/valueThis paper presents a new topology optimization method for the optimal design of 2D and 3D porous materials for extreme elastic properties and macro-structural performance. Unlike previous studies, the presented paper tests the proposed optimization algorithm for not only 2D porous material design but also 3D topology optimization to reveal numerical and computational performance of the used algorithm. In addition, some new and interesting material microstructural topologies have been obtained to provide wider possible solutions to the material design.

Effect of Wick Microstructures on Heat Pipe Performance A Review

The geometry and topology of wick microstructures play a central role in heat pipe performance. It is therefore essential to analyze the wick microstructures. This is accomplished by a twofold approach encompassing wicking capability and thin film evaporation. In this unifying review, individual effects of conduction resistance, thin film percentage area, solid-liquid contact angle, and grooved geometry are collectively discussed. Detailed understanding of the wick characteristics will lead to design of heat pipes with efficient wick structure geometries.

Sliding friction and contact angle hysteresis of droplets on microhole-structured surfaces.

Microstructured surfaces with continuous solid topography have many potential applications in biology and industry. To understand the liquid transport property of microstructured surfaces with continuous solid topography, we studied the sliding behavior of a droplet on microhole-structured surfaces. We found that the sliding friction of the droplet increased with increasing solid area fraction due to enlarged apparent contact area and enhanced contact angle hysteresis. By introducing a correction factor to the modified Cassie-Baxter relation, we proposed an improved theoretical model to better predict the apparent receding contact angle. Our experimental data also revealed that the geometric topology of surface microstructures could affect the sliding friction with microhole-decorated surfaces, exhibiting a larger resistance than that for micropillar-decorated surfaces. Assisted by optical microscopy, we attributed this topology effect to the continuity and the true total length of the three-phase contact line at the receding edge during the sliding. Our study provides new insights into the liquid sliding behavior on microstructured surfaces with different topologies, which may help better design functional surfaces with special liquid transport properties.

Computational networks and systems – homogenization of variational problems on micro-architectured networks and devices

Networked materials and micro-architectured systems gain increasingly importance in multi-scale physics and engineering sciences. Typically, computational intractable microscopic models have to be applied to capture the physical processes and numerous transmission conditions at singularities, interfaces and borders. The topology of the periodic microstructure governs the effective behaviour of such networked systems. A mathematical concept for the analysis of microscopic models on extremely large periodic networks is developed. We consider microscopic models for diffusion–advection–reaction systems in variational form on periodic manifolds. The global characteristics are identified by a homogenization approach for singularly perturbed networks with a periodic topology. We prove that the solutions of the variational models on varying networks converge to a two-scale limit function. In addition, the corresponding tangential gradients converge to a two-scale limit function for vanishing lengths of branches. We identify the variational homogenized model. Complex network models, previously considered as completely intractable, can now be solved by standard PDE-solvers in nearly no time. Furthermore, the homogenized coefficients provide an effective characterization of the global behaviour of the variational system.

Effect of Powder Characteristics and Oxygen Content on Modifications to the Microstructural Topology During Hot Isostatic Pressing of an Austenitic Steel

The effect of powder size distribution and oxygen content on the extent of multiple twinning and spatial distribution of oxide inclusions in hot isostatic pressed (HIPed) 316L steels was investigated using powders with different characteristics. Modifications to, and differences in their microstructural topology, were tracked quantitatively by evaluating the metrics related to twin related domains (TRDs) on specimens produced by interrupting the HIPing process at various points in time. Results revealed that powder size distribution has a strong effect on the extent of multiple twinning in the fully HIPed microstructure, with specimens produced using narrow distribution showing better statistics (i.e., homogeneously recrystallized) than the onesproduced using broad size distribution. The oxide inclusion density in fully HIPed microstructures increased with the amount of oxygen content in the powders while prior particle boundaries (PPBs) were only observed in the specimens that were HIPed using broad powder distribution. More importantly, results clearly revealed that the spatial distribution of the inclusions was strongly affected by the homogeneity of recrystallization. Implications of the results are further discussed in a broader context, emphasizing the importance of utilizing the occurrenceof solid state phase transformations during HIPing for controlling the microstructure evolution.

Multiscale modelling for better hygrothermal prediction of porous building materials

The aim of this work is to understand the influence of the microstructuralgeometric parameters of porous building materials on the mechanisms of coupled heat, air and moisture transfers, in order to predict behavior of the building to control and improve it in its durability. For this a multi-scale approach is implemented. It consists of mastering the dominant physical phenomena and their interactions on the microscopic scale. Followed by a dual-scale modelling, microscopic-macroscopic, of coupled heat, air and moisture transfers that takes into account the intrinsic properties and microstructural topology of the material using X-ray tomography combined with the correlation of 3D images were undertaken. In fact, the hygromorphicbehavior under hydric solicitations was considered. In this context, a model of coupled heat, air and moisture transfer in porous building materials was developed using the periodic homogenization technique. These informations were subsequently implemented in a dynamic computation simulation that model the hygrothermalbehaviourof material at the scale of the envelopes and indoor air quality of building. Results reveals that is essential to consider the local behaviors of materials, but also to be able to measure and quantify the evolution of its properties on a macroscopic scale from the youngest age of the material. In addition, comparisons between experimental and numerical temperature and relative humidity profilesin multilayers wall and in building envelopes were undertaken. Good agreements were observed.

Multiscale modelling for better hygrothermal prediction of porous building materials

The aim of this work is to understand the influence of the microstructuralgeometric parameters of porous building materials on the mechanisms of coupled heat, air and moisture transfers, in order to predict behavior of the building to control and improve it in its durability. For this a multi-scale approach is implemented. It consists of mastering the dominant physical phenomena and their interactions on the microscopic scale. Followed by a dual-scale modelling, microscopic-macroscopic, of coupled heat, air and moisture transfers that takes into account the intrinsic properties and microstructural topology of the material using X-ray tomography combined with the correlation of 3D images were undertaken. In fact, the hygromorphicbehavior under hydric solicitations was considered. In this context, a model of coupled heat, air and moisture transfer in porous building materials was developed using the periodic homogenization technique. These informations were subsequently implemented in a dynamic computation simulation that model the hygrothermalbehaviourof material at the scale of the envelopes and indoor air quality of building. Results reveals that is essential to consider the local behaviors of materials, but also to be able to measure and quantify the evolution of its properties on a macroscopic scale from the youngest age of the material. In addition, comparisons between experimental and numerical temperature and relative humidity profilesin multilayers wall and in building envelopes were undertaken. Good agreements were observed.

Topological shape optimization of 3D micro-structured materials using energy-based homogenization method

This paper proposes an effective method for the design of 3D micro-structured materials to attain extreme mechanical properties, which integrates the firstly developed 3D energy-based homogenization method (EBHM) with the parametric level set method (PLSM). In the 3D EBHM, a reasonable classification of nodes in periodic material microstructures is introduced to develop the 3D periodic boundary formulation consisting of 3D periodic boundary conditions, 3D boundary constraint equations and the reduced linearly elastic equilibrium equation. Then, the effective elasticity properties of material microstructures are evaluated by the average stress and strain theorems rather than the asymptotic theory. Meanwhile, the PLSM is applied to optimize microstructural shape and topology because of its positive characteristics, like the perfect demonstration of geometrical features and high optimization efficiency. Numerical examples are provided to demonstrate the advantages of the proposed design method. Results indicate that the optimized 3D material microstructures with expected effective properties are featured with smooth structural boundaries and clear interfaces.

Analytical transport network theory to guide the design of 3-D microstructural networks in energy materials: Part 1. Flow without reactions

We present a fully analytical, heuristic model – the “Analytical Transport Network Model” – for steady-state, diffusive, potential flow through a 3-D network. Employing a combination of graph theory, linear algebra, and geometry, the model explicitly relates a microstructural network's topology and the morphology of its channels to an effective material transport coefficient (a general term meant to encompass, e.g., conductivity or diffusion coefficient). The model's transport coefficient predictions agree well with those from electrochemical fin (ECF) theory and finite element analysis (FEA), but are computed 0.5–1.5 and 5–6 orders of magnitude faster, respectively. In addition, the theory explicitly relates a number of morphological and topological parameters directly to the transport coefficient, whereby the distributions that characterize the structure are readily available for further analysis. Furthermore, ATN's explicit development provides insight into the nature of the tortuosity factor and offers the potential to apply theory from network science and to consider the optimization of a network's effective resistance in a mathematically rigorous manner. The ATN model's speed and relative ease-of-use offer the potential to aid in accelerating the design (with respect to transport), and thus reducing the cost, of energy materials.

Topology optimization-based design of metamaterial-inspired sensor with improved sensitivity

Sensitivity is of great importance for a Metamaterial (MTM)-inspired sensor in many detecting and sensing applications. In this paper, a new improved sensitivity method for a metamaterial-inspired sensor is proposed, which is based on MTM microstructure topology optimization. The metamaterial-inspired sensor consists of a microstrip-lined excitation and a coupled MTM microstructure, and can be used to dielectric sensing by tracking the resonant frequency shift. The optimization model is established to improve the sensitivity of the sensor where the MTM microstructure is topologically optimized in the design domain. To validate the improved sensitivity, a sensor is designed to monitor the dielectric film thickness. Compared with the complementary split ring resonator (CSRR), complementary single split ring resonator (CSSRR) based sensors, the novel sensor with an optimized MTM exhibits more frequency shift for a tiny variation of the dielectric thickness. The relationship between the dielectric thickness and the resonant frequency is established through polynomial interpolation fitting.

Optimal microstructures of elastoplastic cellular materials under various macroscopic strains

Topology optimization has been applied widely in cellular material design by optimizing the microstructure of periodic base cell (PBC). So far, most works are focused on the design of microstructures with linear material properties using the inverse homogenization method. When accounting elastoplastic constitutive behaviors, there is in usual no overall closed-form constitutive expression for the cellular microstructure as the case of linear elasticity, the design is therefore dependent on the specific applied loading. Due to the importance of topology optimization concerning elastoplastic material, the microstructural topology optimization procedure of elastoplastic cellular material with the objective of maximizing their nonlinear responses in terms of the strain energy density is proposed by using the bi-directional evolutionary structural optimization (BESO) method in this paper. Analytical sensitivity analysis is derived in a clear and rigorous manner using the adjoint method and incorporated into the BESO algorithm. The effectiveness of the proposed approach is validated through a series of numerical examples for various macroscopic strain loadings.

A 3D finite element modelling of crystalline anisotropy in rolling contact fatigue

Rolling contact fatigue (RCF) is one of the primary modes of failure in bearings and in this study it is hypothesized and demonstrated that RCF is strongly influenced by inhomogeneity in polycrystalline material microstructure. This paper presents a three-dimensional modeling approach to include the effects of microstructure topology and material anisotropy in a polycrystalline microstructural bearing steel subject to RCF loading. A randomly generated 3D Voronoi tessellation is used to represent the microstructural topology of the material. A cubic material definition with random spatial orientation is specified for the material grains to simulate the polycrystalline anisotropy. The size of the RVE was chosen such that it represented the macroscopic linear elastic material properties of a polycrystalline aggregate. The semi-infinite domain is then subjected to a moving Hertzian pressure to simulate a load cycle. Due to inhomogeneity in the polycrystalline material local stress risers occur at the grain boundaries, however, in general, the locations of the maximum shear stresses compare well to the experimental RCF results readily available in literature. Elemental shear stresses averaging scheme was employed to illustrate that the finite element model is mesh independent. The estimated fatigue life scatter obtained from the inhomogeneous polycrystalline material model corroborates well with the fatigue life scatter obtained from the RCF experiments.

Multiscale modeling of carbon nanotube reinforced concrete

The present paper proposes a hierarchical multiscale approach in order to evaluate the nonlinear constitutive behavior of concrete reinforced with carbon nanotubes (CNTs). To this purpose, representative volume elements, consistent to the microstructural topology of the material, are constructed and analyzed using finite elements. As the dimensions of the CNTs and those of a typical mesoscale concrete RVE differ by orders of magnitude, a hierarchical multiscale analysis strategy is implemented to pass information through scales with different RVEs assigned at each scale of separation. Both elastic and inelastic analyses are performed on all scales for various CNT weight fractions, defining a different nonlinear constitutive stress–strain behavior at each scale of separation. It is shown that the proposed computational approach can be used alternatively to corresponding costly experiments in order to accurately evaluate the nonlinear constitutive behavior of such complex materials.

Meso and Microstructural Interactions in Porous Lithium-Ion Batteries

Rechargeable batteries are porous electrochemical structures composed of secondary particles, which are aggregates of single crystal primary particles, pores, cracks, and processing-induced phases and features. The underlying meso and microstructural topology, including its size, size distribution, morphology and crystallographic orientation of each of the underlying phases impacts the delivered power and energy density. While it is clear that the component with the lowest efficiency will be the bottleneck to performance of the overall device, the understanding of the fundamentals associated to the different electrochemical and chemomechanical interactions of the underlying phases remains unclear. In this paper we will discuss the meso and microstructural limitations associated to porous cathode electrodes, and will outline strategies to tune the response of primary and secondary particle configurations for high power or energy density applications.

Crack incubation in shot peened AA7050 and mechanism for fatigue enhancement

AbstractShot peening is a dynamic cold‐working process involving the impingement of peening media onto a substrate surface. Shot peening is commonly used as a surface treatment technique within the aerospace industry during manufacturing to improve fatigue performance of structural components. The compressive residual stress induced during shot peening results in fatigue crack growth retardation, improving the performance of shot‐peened components. However, shot peening is a compromise between the benefit of inducing a compressive residual stress and causing detrimental surface damage. Because of the relatively soft nature of AA7050‐T7451, shot peening can result in cracking of the constituent precipitate particles, creating an initial damage state. The aim of this paper is to understand the balance and fundamentals of these competing phenomena through a comparative study throughout the fatigue lifecycle of baseline versus shot‐peened AA7050‐T7451. Microstructure and surface topology characterization and comparison of the baseline and shot‐peened AA7050‐T7451 has been performed using scanning electron microscopy, electron backscatter diffraction, energy dispersive spectroscopy, and optical profilometry techniques. A residual stress analysis through interrupted fatigue of the baseline and shot‐peened AA7050‐T7451 was completed using a combination of X‐ray diffraction and nanoindentation. The fatigue life performance of the baseline versus shot‐peened material has been evaluated, including crack initiation and propagation. Subsurface particles crack upon shot peening but did not incubate into the matrix during fatigue loading, presumably due to the compressive residual stress field. In the baseline samples, the particles were initially intact, but upon fatigue loading, crack nucleation was observed in the particles, and these cracks incubated into the matrix. In damage tolerant analysis, an initial defect size is needed for lifetime assessment, which is often difficult to determine, leading to overly conservative evaluations. This work provides a critical assessment of the mechanism for shot peening enhancement for fatigue performance and quantifies how incubation of a short crack is inhibited from an initially cracked particle into the matrix within a residual stress field.